Question

(related rates problem please help!)
A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant.

Answer 1

Given:
\(dV/dt=kr^2\)
From \(\large V=\frac{4\pi r^3}{3}\)
we have \(\large \frac{dV}{dr}=4\pi r^2\)
\(\large dr/dt=dr/dV*dV/dt=\frac{1}{4\pi r^2}*kr^2=\frac{k}{4\pi}=constant\)